Parametric Methodology in Optimization

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Questions about what happens to a solution to a problem of optimization when the parameters on which the problem depends are perturbed are important not only in assessing the stability of mathematical models, but also in the design and justification of computational procedures. Issues of parametric dependence are also the key to effective utilization of `cost-to-go' functions in dynamical optimization, whether in optimal control or stochastic programming. This project would advance the methodology for dealing with such dependence and explore its consequences for computation.The latest tools in variational analysis, which are essential becauseof inherent nonsmoothness in parametric dependence, would be applied.Alternative forms of optimality conditions, focused especially on perturbational robustness, would be investigated in a broad framework,both finite- and infinite-dimensional. Cost-to-go functions in convexdynamical optimization would be studied from the new perspective both in deterministic continuous-time models, with their connections to Hamilton-Jacobi theory, and in stochastic discrete-time models, wherethe numerical potential will dominate.